JIPMAT 2024 (QA) - Given below are two statements : that a: b=5: 3 and b: c=2: 5, then ( c-a ) will be equal to I: 10(a+c) Statement II: 10 a+25 b In the light of the above statements, choose the correct answer from the options given below : | PYQs + Solutions

JIPMAT 2024

Arithmetic

Ratio, Proportion & Variation

Medium

Given below are two statements :
Given that $a: b=5: 3$ and $b: c=2: 5$ , then ( $c-a$ ) will be equal to
Statement I: $10(a+c)$ $\newline$ Statement II: $10 a+25 b$
In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Correct Option: 2

Let me solve this step by step.

1) Given ratios:

\newline

a:b = 5:3

\newline

b:c = 2:5

2) From first ratio

\frac{a}{b} = \frac{5}{3}

\newline

* If we take

b = 6

(to make calculations easier)

\newline

* Then

a = 10

\newline

* These values maintain the ratio

5:3

3) From second ratio

\frac{b}{c} = \frac{2}{5}

\newline

* With

b = 6

\newline

* Then

c = 15

\newline

* These values maintain the ratio

2:5

4) Now we can find

(c-a)

\newline

c-a = 15-10 = 5

5) Let's check Statement I:

\newline

10(a+c)

\newline

10(10+15)

\newline

10(25)

\newline

250

\newline

This is not equal to

(c-a) = 5

6) Let's check Statement II:

\newline

10a+25b

\newline

10(10)+25(6)

\newline

100+150

\newline

250

\newline

This is not equal to

(c-a) = 5

Therefore, both statements are false.